Discreteness of log discrepancies over log canonical triples on a fixed pair
Author:
Masayuki Kawakita
Journal:
J. Algebraic Geom. 23 (2014), 765-774
DOI:
https://doi.org/10.1090/S1056-3911-2014-00630-5
Published electronically:
February 25, 2014
MathSciNet review:
3263668
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Abstract |
References |
Additional Information
Abstract: For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.
References
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- Caucher Birkar, Paolo Cascini, Christopher D. Hacon, and James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468. MR 2601039, DOI https://doi.org/10.1090/S0894-0347-09-00649-3
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- Tommaso de Fernex and Mircea Mustaţă, Limits of log canonical thresholds, Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), no. 3, 491–515 (English, with English and French summaries). MR 2543330, DOI https://doi.org/10.24033/asens.2100
- Lawrence Ein and Mircea Mustaţǎ, Inversion of adjunction for local complete intersection varieties, Amer. J. Math. 126 (2004), no. 6, 1355–1365. MR 2102399
- Masayuki Kawakita, Towards boundedness of minimal log discrepancies by the Riemann-Roch theorem, Amer. J. Math. 133 (2011), no. 5, 1299–1311. MR 2843100, DOI https://doi.org/10.1353/ajm.2011.0037
- Masayuki Kawakita, Ideal-adic semi-continuity problem for minimal log discrepancies, Math. Ann. 356 (2013), no. 4, 1359–1377. MR 3072804, DOI https://doi.org/10.1007/s00208-012-0885-y
- J. Kollár, Which powers of holomorphic functions are integrable?, arXiv:0805.0756
- V. V. Shokurov, Problems about Fano varieties, Birational geometry of algebraic varieties, Open problems, Katata 1988, pp. 30-32
- V. V. Shokurov, $3$-fold log models, J. Math. Sci. 81 (1996), no. 3, 2667–2699. Algebraic geometry, 4. MR 1420223, DOI https://doi.org/10.1007/BF02362335
- V. V. Shokurov, Letters of a bi-rationalist. V. Minimal log discrepancies and termination of log flips, Tr. Mat. Inst. Steklova 246 (2004), no. Algebr. Geom. Metody, Svyazi i Prilozh., 328–351 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 3(246) (2004), 315–336. MR 2101303
- Michael Temkin, Desingularization of quasi-excellent schemes in characteristic zero, Adv. Math. 219 (2008), no. 2, 488–522. MR 2435647, DOI https://doi.org/10.1016/j.aim.2008.05.006
References
- Florin Ambro, On minimal log discrepancies, Math. Res. Lett. 6 (1999), no. 5-6, 573–580. MR 1739216 (2001c:14031)
- Caucher Birkar, Paolo Cascini, Christopher D. Hacon, and James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468. MR 2601039 (2011f:14023), DOI https://doi.org/10.1090/S0894-0347-09-00649-3
- Tommaso de Fernex, Lawrence Ein, and Mircea Mustaţă, Shokurov’s ACC conjecture for log canonical thresholds on smooth varieties, Duke Math. J. 152 (2010), no. 1, 93–114. MR 2643057 (2011c:14036), DOI https://doi.org/10.1215/00127094-2010-008
- Tommaso de Fernex, Lawrence Ein, and Mircea Mustaţă, Log canonical thresholds on varieties with bounded singularities, Classification of algebraic varieties, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2011, pp. 221–257. MR 2779474 (2012f:14020), DOI https://doi.org/10.4171/007-1/10
- Tommaso de Fernex and Mircea Mustaţă, Limits of log canonical thresholds, Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), no. 3, 491–515 (English, with English and French summaries). MR 2543330 (2010i:14030)
- Lawrence Ein and Mircea Mustaţǎ, Inversion of adjunction for local complete intersection varieties, Amer. J. Math. 126 (2004), no. 6, 1355–1365. MR 2102399 (2005j:14020)
- Masayuki Kawakita, Towards boundedness of minimal log discrepancies by the Riemann-Roch theorem, Amer. J. Math. 133 (2011), no. 5, 1299–1311. MR 2843100 (2012h:14032), DOI https://doi.org/10.1353/ajm.2011.0037
- Masayski Kawakita, Ideal-adic semi-continuity problem for minimal log discrepancies, Math. Ann. 356 (2013), no. 4, 1359–1377. DOI 10.1007/s00208-012-0885-y. MR 3072804
- J. Kollár, Which powers of holomorphic functions are integrable?, arXiv:0805.0756
- V. V. Shokurov, Problems about Fano varieties, Birational geometry of algebraic varieties, Open problems, Katata 1988, pp. 30-32
- V. V. Shokurov, $3$-fold log models, J. Math. Sci. 81 (1996), no. 3, 2667–2699. Algebraic geometry, 4. MR 1420223 (97i:14015), DOI https://doi.org/10.1007/BF02362335
- V. V. Shokurov, Letters of a bi-rationalist. V. Minimal log discrepancies and termination of log flips, Tr. Mat. Inst. Steklova, Algebr. Geom. Metody, Svyazi i Prilozh. 246 (2004), 328–351 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 246 (2004), no. 3, 315–336. MR 2101303 (2006b:14019)
- Michael Temkin, Desingularization of quasi-excellent schemes in characteristic zero, Adv. Math. 219 (2008), no. 2, 488–522. MR 2435647 (2009h:14027), DOI https://doi.org/10.1016/j.aim.2008.05.006
Additional Information
Masayuki Kawakita
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
MR Author ID:
680001
Email:
masayuki@kurims.kyoto-u.ac.jp
Received by editor(s):
May 3, 2012
Received by editor(s) in revised form:
August 22, 2012, and September 11, 2012
Published electronically:
February 25, 2014
Additional Notes:
Partial support was provided by Grant-in-Aid for Young Scientists (A) 24684003.
Article copyright:
© Copyright 2014
University Press, Inc.